User:Unque/5L 3s Tonal Theory: Difference between revisions
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Added formulas for scale degrees |
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== Defining Terms == | == Defining Terms == | ||
For the purposes of this page, I will be describing the degrees of the Oneiro scale using a system based on a system of seven nominals and one interordinal; this allows for the octave to land on the interval of equivalence, maintaining the octave complement relationships (e.g. m7 ~ M2, M3 ~ m6, etc.) | For the purposes of this page, I will be describing the degrees of the Oneiro scale using a system based on a system of seven nominals and one interordinal; this allows for the octave to land on the interval of equivalence, maintaining the octave complement relationships (e.g. m7 ~ M2, M3 ~ m6, etc.). Each scale degree has a distinct formula, allowing a composer to find the exact size of any degree by only knowing the size of L and s. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Degrees of Oneiro | |+Degrees of Oneiro | ||
!Degree | !Degree | ||
!Formula | |||
!Soft Range | !Soft Range | ||
!Hard Range | !Hard Range | ||
| Line 16: | Line 17: | ||
|- | |- | ||
|1 | |1 | ||
|N/A | |||
|1/1 | |1/1 | ||
|1/1 | |1/1 | ||
| Line 22: | Line 24: | ||
|- | |- | ||
|chroma | |chroma | ||
|L - s | |||
|1/13 - 1\5 | |1/13 - 1\5 | ||
|1/1 - 1\13 | |1/1 - 1\13 | ||
| Line 28: | Line 31: | ||
|- | |- | ||
|m2 | |m2 | ||
|s | |||
|1/1 - 1\13 | |1/1 - 1\13 | ||
|1\13 - 1\8 | |1\13 - 1\8 | ||
| Line 34: | Line 38: | ||
|- | |- | ||
|M2 | |M2 | ||
|L | |||
|2\13 - 1\5 | |2\13 - 1\5 | ||
|1\8 - 2\13 | |1\8 - 2\13 | ||
| Line 40: | Line 45: | ||
|- | |- | ||
|m3 | |m3 | ||
|L + s | |||
|1\5 - 2\8 | |1\5 - 2\8 | ||
|3\13 - 1\4 | |3\13 - 1\4 | ||
| Line 46: | Line 52: | ||
|- | |- | ||
|M3 | |M3 | ||
|L + L | |||
|4\13 - 2\5 | |4\13 - 2\5 | ||
|1\4 - 4\13 | |1\4 - 4\13 | ||
| Line 52: | Line 59: | ||
|- | |- | ||
|d4 | |d4 | ||
|L + 2s | |||
|1\5 - 4\13 | |1\5 - 4\13 | ||
|4\13 - 3\8 | |4\13 - 3\8 | ||
| Line 58: | Line 66: | ||
|- | |- | ||
|P4 | |P4 | ||
|2L + s | |||
|5\13 - 2\5 | |5\13 - 2\5 | ||
|3\8 - 5\13 | |3\8 - 5\13 | ||
| Line 64: | Line 73: | ||
|- | |- | ||
|t | |t | ||
|2L + 2s | |||
|2\5 - 6\13 | |2\5 - 6\13 | ||
|6\13 - 1\2 | |6\13 - 1\2 | ||
| Line 70: | Line 80: | ||
|- | |- | ||
|T | |T | ||
|3L + s | |||
|7\13 - 3\5 | |7\13 - 3\5 | ||
|1\2 - 7\13 | |1\2 - 7\13 | ||
| Line 76: | Line 87: | ||
|- | |- | ||
|P5 | |P5 | ||
|3L + 2s | |||
|3\5 - 8\13 | |3\5 - 8\13 | ||
|8\13 - 5\8 | |8\13 - 5\8 | ||
| Line 82: | Line 94: | ||
|- | |- | ||
|A5 | |A5 | ||
|4L + s | |||
|9\13 - 4\5 | |9\13 - 4\5 | ||
|5\8 - 9\13 | |5\8 - 9\13 | ||
| Line 88: | Line 101: | ||
|- | |- | ||
|m6 | |m6 | ||
|3L + 3s | |||
|3\5 - 9\13 | |3\5 - 9\13 | ||
|9\13 - 3\4 | |9\13 - 3\4 | ||
| Line 94: | Line 108: | ||
|- | |- | ||
|M6 | |M6 | ||
|4L + 2s | |||
|10\13 - 4\5 | |10\13 - 4\5 | ||
|3\4 - 10\13 | |3\4 - 10\13 | ||
| Line 100: | Line 115: | ||
|- | |- | ||
|m7 | |m7 | ||
|4L + 3s | |||
|4\5 - 11\13 | |4\5 - 11\13 | ||
|11\13 - 7\8 | |11\13 - 7\8 | ||
| Line 106: | Line 122: | ||
|- | |- | ||
|M7 | |M7 | ||
|5L + 2s | |||
|12\13 - 2/1 | |12\13 - 2/1 | ||
|7\8 - 12\13 | |7\8 - 12\13 | ||
| Line 112: | Line 129: | ||
|- | |- | ||
|8 | |8 | ||
|5L + 3s | |||
|2/1 | |2/1 | ||
|2/1 | |2/1 | ||